Mirrors and reflections: the geometry of finite reflection groups
β Scribed by Alexandre V. Borovik, Anna Borovik
- Book ID
- 127397195
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 670 KB
- Series
- Pharmaceutical Science Series
- Edition
- 1
- Category
- Library
- ISBN
- 0387790659
No coin nor oath required. For personal study only.
β¦ Synopsis
Mirrors and Reflections is a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups.
Key features: β’ Many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theoryβ’ A large number of exercises at various levels of difficultyβ’ Some Euclidean geometry is included along with the theory of convex polyhedraβ’ Few prerequisites are necessary beyond linear algebra and the basic notions of group theory.
The exposition is directed at advanced undergraduates and first-year graduate students.
π SIMILAR VOLUMES
Let G be a finite group of complex n = n unitary matrices generated by reflections acting on β«ήβ¬ n . Let R be the ring of invariant polynomials, and let be a multiplicative character of G. Let β be the R-module of -invariant differential forms. We define a multiplication in β and show that under thi
Any finite reflection group G admits a distinguished basis of G-invariants canonically attached to a certain system of invariant differential equations. We determine it explicitly for groups of types A, B, D, and I in a systematic way.